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Coefficient of Determination quiz

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  • What does the coefficient of determination (R^2) measure in a dataset?
    It measures how much of the variation in the dependent variable (y) is explained by the independent variable (x).
  • How is the coefficient of determination (R^2) related to the linear correlation coefficient (r)?
    R^2 is simply the square of the linear correlation coefficient r.
  • What is the range of possible values for R^2?
    R^2 ranges from 0 to 1.
  • If R^2 is close to 1, what does this indicate about the data?
    It indicates that most of the variation in y is explained by the linear relationship with x.
  • If R^2 is close to 0, what does this indicate about the data?
    It means that very little of the variation in y is explained by x; most variation is unexplained.
  • How do you calculate R^2 if you are given the value of r?
    You calculate R^2 by squaring the value of r.
  • What is the formula for R^2 in terms of variation?
    R^2 = explained variation / total variation.
  • How is explained variation defined in the context of R^2?
    Explained variation is the sum of squared distances from the regression line to the mean of y.
  • How is total variation defined when calculating R^2?
    Total variation is the sum of squared distances from each data point to the mean of y.
  • Why is R^2 always a positive number?
    Because it is the square of r, and squaring any real number results in a non-negative value.
  • How are R^2 values typically expressed in interpretation?
    They are usually expressed as percentages, indicating the percent of variation explained.
  • What does the complement of R^2 represent in a dataset?
    It represents the percentage of variation in y that is unexplained by x, due to randomness or other factors.
  • What does it mean graphically if data points are close to the regression line?
    It means R^2 is high, indicating a strong linear relationship.
  • What does it mean if data points are widely scattered from the regression line?
    It means R^2 is low, indicating a weak or no linear relationship.
  • How can you find R^2 using a graphing calculator?
    Input the data, use the linear regression function, and the calculator will display both r and R^2.